Research On Stability Analysis And Synthesis Of Several Hybrid Systems Based On LMI

Hybrid systems are composed of discrete event dynamic systems and continuous variable dynamic systems, which interact on each other. The appearance of hybrid system resulted from the combination of various disciplines such as control theory, computer science, system science and mathematics. The theory of hybrid systems is demand of further development of traditional control theory. On the other hand, recent technological innovations have caused a considerable interest in the study of dynamical processes having a heterogeneous continuous and discrete nature. Many real-world systems such as embedded systems, communication networks, electric power systems, chemical processes, traffic control, robotics, can be modelled as hybrid systems. In conclusion, the research of hybrid systems is significant for both theory and practice.Based on Lyapunov stability theory of hybrid systems and using linear matrix inequalities method, this dissertation mainly investigates the stability analysis and synthesis of several hybrid systems from the control point of view. On the side of stability analysis, some typical hybrid systems, such as switched systems with time delay, a class of hybrid Systems with nonlinear uncertainty and piecewise linear affine systems, were addressed. On the side of synthesis, this thesis studied some problems of discrete switched systems with time delay, such as state feedback stabilization, output feedback stabilization and H_∞ control. The main contributions of this dissertation are as follows:1. First, the asymptotic stability of continuous switched systems with time delay is studied. A convex combination condition and a switching strategy are derived. Second, the asymptotic stability of discrete switched systems with time delay is studied. Two different sufficient conditions are derived for the asymptotic stability under arbitrary switching. Further, the convex combination conditions for asymptotic stability of such system and a switching strategy are developed.2. A new sufficient condition under arbitrary switching for asymptotic stability of discrete switched systems with single time-delay is proposed. Furthermore, a memoryless state feedback and a memoryless output feedback stabilization for such switched systems are established. Finally, these results are extended to uncertain switched systems with time-delay.3. The problem of feedback stabilization for discrete switched systems with multi-time-delay subsystems is addressed. Switched systems with time delay can be converted into switched systems without time delay by state transformation.Based on previous work, some state feedback methods and output feedback methods with memory are established respectively in terms of linear matrix inequalities. These results are extended to uncertain switched systems with multi-time-delay.4. A new sufficient condition of the Hoc performance analysis under arbitrary switching for discrete switched systems with time delay and disturbance is derived. This thesis proposed a memory Hoo controller and a memoryless Hoo controller via state feedback. These results are extended to uncertain switched systems with time delay.5. This paper investigates the stability of a class of continuous hybrid systems with nonlinear uncertainty. Based on common Lyapunov function, the sufficient conditions of such system for global asymptotic stability are proposed. Furthermore, using the method of piecewise quadratic Lyapunov function, the sufficient conditions of such system for local asymptotic stability are derived. These results are extended to discrete hybrid systems.6. Based on continuous piecewise quadratic Lyapunov function, the sufficient conditions of uncertain continuous and discrete piecewise linear affine systems are given. With the same idea, the sufficient conditions of continuous and discrete piecewise linear affine systems, which is delay-dependent or delay-independent, are proposed.